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Game Theory

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Theory of Games and Economic Behavior

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Author: John von Neumann

This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

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Chaotic Elections! A Mathematician Looks at Voting

Chaotic Elections! A Mathematician Looks at Voting List price: $25.00
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Author: Donald G. Saari

What does the 2000 U.S. presidential election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts, or defective ballots, but are caused by the very way Americans vote for president.

This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described.

Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase "what the voters really want" might mean and obtain a unique voting method that satisfies these conditions.

Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes.

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Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics

Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics List price: $153.99
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Author: Thomas L. Vincent

All of life is a game and evolution by natural selection is no exception. The evolutionary game theory developed in this book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.

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The S.E.X. Blackjack System

The S.E.X. Blackjack System List price: $12.95
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Author: Alan Mandel

Game Theory and its Applications, Second Edition: in the Social and Biological Sciences (International Series in Social Psychology)

Game Theory and its Applications, Second Edition: in the Social and Biological Sciences (International Series in Social Psychology) List price: $31.95
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Author: Andrew Colman

This thoroughly revised edition of the critically acclaimed 'Game Theory and Experimental Games: The Study of Strategic Interaction' provides a user-friendly
introduction to the fundamental ideas of mathematical game theory together with a comprehensive survey of experimental gaming and other major applications in social psychology, decision theory, economics, politics, evolutionary biology, philosophy,
operational research and sociology.

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An Introduction to Game-Theoretic Modelling

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Author: Michael Mesterton-Gibbons

This book is about using game theory in mathematical modelling. It is an introductory text, covering the basic ideas and methods of game theory as well as the necessary ideas from the vast spectrum of scientific study where the methods are applied.

It has by now become generally apparent that game theory is a fascinating branch of mathematics with both serious and recreational applications. Strategic behavior arises whenever the outcome of an individual's action depends on actions to be taken by other individuals--whether human, as in the Prisoners' Dilemma, or otherwise, as in the "duels of damselflies". As a result, game-theoretic mathematical models are applicable in both the social and natural sciences. In reading this book, you can learn not just about game theory, but also about how to model real situations so that they can be analyzed mathematically.

Mesterton-Gibbons includes the familiar game theory examples where they are needed for explaining the mathematics or when they provide a valuable application. There are also plenty of new examples, in particular from biology, such as competitions for territory or mates, games among kin versus games between kin, and cooperative wildlife management.

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Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them (Classroom Resource Materials)

Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them (Classroom Resource Materials) List price: $46.50
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Author: John O. Kiltinen

Popular puzzles such as the Rubik's cube and so-called oval track puzzles give a concrete representation to the theory of permutation groups. They are relatively simple to describe in group theoretic terms, yet present a challenge to anyone trying to solve them. John Kiltinen shows how the theory of permutation groups can be used to solve a range of puzzles. There is also an accompanying CD that can be used to reduce the need for carrying out long calculations and memorising difficult sequences of moves. This book will prove useful as supplemental material for students taking abstract algebra courses. It provides a real application of the theory and methods of permutation groups, one of the standard topics. It will also be of interest to anyone with an interest in puzzles and a basic grounding in mathematics. The author has provided plenty of exercises and examples to aid study.

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Games of No Chance (Mathematical Sciences Research Institute Publications)

Games of No Chance (Mathematical Sciences Research Institute Publications) List price: $130.00
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Is Nine-Men's Morris, in the hands of perfect players, a win for white or for black--or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full anlaysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men's Morris and Pentominoes; and new theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.

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Differential Games and Applications (Lecture Notes in Control and Information Sciences, Vol 119)

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Author: T.S. Basar

Differential Games: Developments in Modelling and Computation : Proceedings of the 4th International Symposium on Differential Games and Applications (Lecture ... Notes in Control and Information Sciences)

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Author: R. P. Hamalainen

This collection of articles indicates that there is a strong new boom of interest in the area of dynamic games. The papers included in this volume are designed to serve as a source of problem formulations and references for established researchers as well as for new researchers who are entering this field. In these proceedings, the papers have been grouped into four sections dealing with zero-sum differential games of pursuit evasion type and their application to aerospace problems, search and discrete games, robust controller design and numerical and hierarchical methods.

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